Radial Basis Function Solution of the Motz Problem Articles uri icon

publication date

  • January 2010

start page

  • 606

end page

  • 620

issue

  • 5

volume

  • 27

international standard serial number (ISSN)

  • 0264-4401

electronic international standard serial number (EISSN)

  • 1758-7077

abstract

  • Purpose: The Motz problem can be considered as a benchmark problem for testing the performance of numerical methods in the solution of elliptic problems with boundary singularities. The purpose of this paper is to address the solution of the Motz problem using the radial basis function (RBF) method, which is a truly meshfree scheme. Design/methodology/approach: Both the global RBF collocation method (also known as Kansa's method) and the recently proposed local RBF-based differential quadrature (LRBFDQ) method are considered. In both cases, it is shown that the accuracy of the solution can be significantly increased by using special functions which capture the behavior of the singularity. In the case of global collocation, the functional space spanned by the RBF is enlarged by adding singular functions which capture the behavior of the local singular solution. In the case of local collocation, the problem is modified appropriately in order to eliminate the singularities from the formulation.